Free Layer Thickness Dependence of the Stability in Co2(Mn0.6Fe0.4)Ge Heusler Based CPP-GMR Read Sensor for Areal Density of 1 Tb/in2

Current-perpendicular-to-the-plane giant magnetoresistance (CPP-GMR) read sensors based on Heusler alloys are promising candidates for ultrahigh areal densities of magnetic data storage technology. In particular, the thickness of reader structures is one of the key factors for the development of practical CPP-GMR sensors. In this research, we studied the dependence of the free layer thickness on the stability of the Co2(Mn0.6Fe0.4)Ge Heusler-based CPP-GMR read head for an areal density of 1 Tb/in2, aiming to determine the appropriate layer thickness. The evaluations were done through simulations based on micromagnetic modelling. The reader stability indicators, including the magnetoresistance (MR) ratio, readback signal, dibit response asymmetry parameter, and power spectral density profile, were characterized and discussed. Our analysis demonstrates that the reader with a free layer thickness of 3 nm indicates the best stability performance for this particular head. A reasonably large MR ratio of 26% was obtained by the reader having this suitable layer thickness. The findings can be utilized to improve the design of the CPP-GMR reader for use in ultrahigh magnetic recording densities.

In the past few decades, the outstanding features of the CPP-GMR reader, i.e., large magnetoresistive (MR) outputs, extremely low resistance area (RA) product, capability of transferring large amounts of data at high speeds, and low thermal fluctuation, have been extensively proved [2,[7][8][9]. The very low RA product of the CPP-GMR devices is a key factor in achieving significantly higher ADs than the tunnel magnetoresistance (TMR) junctions used in the current situation [10][11][12][13]. The CPP-GMR sensors based on ferromagnetic Heusler alloys are the most capable integrations that can provide very high performance of CPP-GMR sensors nowadays [14][15][16][17][18][19]. Therefore, several studies have attempted to improve the MR output of the CPP-GMR sensors using various Heusler alloy compositions; however, recent studies indicate that using the Co 2 (Mn 0.6 Fe 0.4 )Ge (CMFG) Heusler alloy as the sensing layer electrodes could provide the highest MR output [20][21][22][23].
At ultrahigh ADs in which the media bits must be rapidly downsized, the physical size of the reader needs to be reduced to prevent intertrack interference while maintaining adequate resolution [1,[24][25][26]. The reader shield-to-shield spacing (SSS) is one of the structural parameters directly related to the physical dimension of the head. It also has a major impact on the down-track resolution. Therefore, reducing the SSS is a crucial point for increasing the AD. At an AD of 1 Tb/in 2 , the SSS was expected to be less than 25 nm [26]. In particular, the thickness of reader layers is a relative sizing parameter of the SSS. A few nanometers of layers embedded in reader structures are typically desired for the development of practical CPP-GMR read sensors, especially at higher ADs. It is well-known that the thickness of the reader layers also has an influential impact on head performance, particularly the stability of head response [14,27,28]. Thus, the suitable thickness of the head layers should be precisely designed for each one.
In this work, we studied the dependence of the free layer thickness of the CPP-GMR reader on the head's stability performance. The CPP-GMR head based on the CMFG Heusler alloy was focused, assuming that the head was targeted for AD of 1 Tb/in 2 . Micromagnetic simulations were based on the finite element method using the M3 code [29]. The rest of this paper is arranged as follows: CPP-GMR modelling is shown in Section 2. Section 3 describes the analysis of read head response. The simulation results, including the related discussions, are given in Section 4. Finally, the results are concluded in Section 5.

CPP-GMR Modelling
As shown in Figure 1a, the sensing layers of the CPP-GMR read head targeted for AD of 1 Tb/in 2 are modelled, assuming that the head is sensing the magnetic stray field, H stray , of the medium. The reader width and stripe height of the head were set at 60 and 48 nm, respectively, since this dimension was claimed as the appropriate value for the CPP-GMR reader at an AD of 1 Tb/in 2 [30]. The combination of the CMFG electrodes and AgSn/InZnO spacer was performed due to their suitability for practical CPP-GMR devices [15]. The thickness of the bottom reference layer was 5 nm, while that of the spacer was 2.1 nm. The free layer thickness, t FL , was the main variable in this study, it was varied from 1 to 10 nm. The magnetization of the free layer, M free , was along its easy axis (+y-axis), while the magnetization of the reference layer, M ref , was fixed along the +x-axis, assuming that it is due to the exchange bias effect of the anti-ferromagnetic layer. The H stray produced by the medium was applied to the head on the air bearing surface (x-axis) to mimic the reading situation. The hard bias field, H B , was uniformly supplied to the reader to provide a ±30 • tilted angle of the free layer magnetization while receiving the H stray . The magnetic media was assumed to be a perpendicular medium having a 10 nm hard layer, while a bit aspect ratio of 4 was set. The medium was based on FePt since it has been widely claimed as a promising material for overcoming the thermal stability limitation at high recording capacities [31,32]. The cross-track magnetic bits are shown in Figure 1b. Their sequence was generated by the 63 pseudorandom bit sequence (PRBS) using the x 6 + x 5 + 1 generator polynomial [33]. The gray-and white-filled bits indicate the direction of H stray along the +x and −x axis, respectively. It is noted that there are no writing errors or intertrack interference included in the simulations, therefore there is no transition noise. The head was assumed to be operated at 1 GHz for practical reasons.
The magnetic properties of CMFG Heusler alloy are adopted from reference [15], as follows: saturation magnetization of 10 × 10 5 A/m, anisotropy constant of 8 × 10 3 J/m 3 , spin polarization factor of 0.76, Gilbert damping parameter of 0.01, and exchange stiffness constant of 2.25 × 10 −11 J/m. The RA product of the sensing layers was 0.11 Ωµm 2 . The head was biased with the bias current density of 1.96 × 10 6 A/cm 2 , where its magnitude was purposely limited in order to minimize the influence of spin torque induced instabilities from this current. A positive sign of bias current is when it flows from the reference to the free layers. The device was assumed to be operated at room temperature. The timevarying magnetization was described using the Landau-Lifshitz-Gilbert-Slonczewski (LLGS) formula, as expressed in references [34,35]. A computational cell size of 2.5 × 2.5 × 2.5 nm 3 and a time step of 0.1 ps were set in the simulations. The magnetic properties of CMFG Heusler alloy are adopted from reference [15], follows: saturation magnetization of 10 × 10 5 A/m, anisotropy constant of 8 × 10 3 J/m 3 , sp polarization factor of 0.76, Gilbert damping parameter of 0.01, and exchange stiffness co stant of 2.25 × 10 −11 J/m. The RA product of the sensing layers was 0.11 Ωμm 2 . The hea was biased with the bias current density of 1.96 × 10 6 A/cm 2 , where its magnitude w purposely limited in order to minimize the influence of spin torque induced instabiliti from this current. A positive sign of bias current is when it flows from the reference to th free layers. The device was assumed to be operated at room temperature. The time-var ing magnetization was described using the Landau-Lifshitz-Gilbert-Slonczewski (LLG formula, as expressed in references [34,35]. A computational cell size of 2.5 × 2.5 × 2.5 nm and a time step of 0.1 ps were set in the simulations.

Analysis of Read Head Response
It is well known that a few nanometers of thickness layers typically have an influe tial impact on the read head performance, especially at higher ADs. Therefore, the lay thickness of Heusler alloy films embedded in the CPP-GMR structure needs to be op mally designed to achieve the desired physical dimension of practical CPP-GMR sensor To investigate the dependence of free layer thickness on the CPP-GMR reader's stabili performance, the output characteristics of the head, including the MR ratio, readback si nal, dibit response, asymmetry parameter, and power spectral density (PSD) profile, we analyzed and discussed. The MR ratio basically represents the amplitude of the sensor output. The readback signal typically indicates the head response. It is obtained from th magnetization dynamic of the free layer passing through the Butterworth low-pass filt [36]. Based on the readback signal pattern, the dibit response is another important param eter indicating the nonlinear behavior and distortion occurring in the readback waveform In this work, we performed the domain dibit extraction technique to obtain the linear dib response as well as the nonlinearities via echoes around the main pulses [37]. In additio an asymmetry parameter can be calculated from the difference between the positive an negative readback amplitudes, as written in Equation (1)

Analysis of Read Head Response
It is well known that a few nanometers of thickness layers typically have an influential impact on the read head performance, especially at higher ADs. Therefore, the layer thickness of Heusler alloy films embedded in the CPP-GMR structure needs to be optimally designed to achieve the desired physical dimension of practical CPP-GMR sensors. To investigate the dependence of free layer thickness on the CPP-GMR reader's stability performance, the output characteristics of the head, including the MR ratio, readback signal, dibit response, asymmetry parameter, and power spectral density (PSD) profile, were analyzed and discussed. The MR ratio basically represents the amplitude of the sensor's output. The readback signal typically indicates the head response. It is obtained from the magnetization dynamic of the free layer passing through the Butterworth low-pass filter [36]. Based on the readback signal pattern, the dibit response is another important parameter indicating the nonlinear behavior and distortion occurring in the readback waveform. In this work, we performed the domain dibit extraction technique to obtain the linear dibit response as well as the nonlinearities via echoes around the main pulses [37]. In addition, an asymmetry parameter can be calculated from the difference between the positive and negative readback amplitudes, as written in Equation (1) [38].
The PSD profile demonstrates the fluctuation of the time-varying magnetization, as well as indicates the frequency spectrum of the readback signal. The local PSD is firstly calculated through the time-varying magnetization, M x,y,z (r i ,t j ), where r i is the magnetization position at each varying time, t j , given in Equation (2) [39]. Then, the total PSD was computed by a summation of the local PSD at each particular frequency, S x,y,z (r i , f ), given as Equation (3). An integrated PSD can be further obtained by an integral of the overall PSD.

Results and Discussion
In this section, the output characteristics of the CPP-GMR read head were characterized at different t FL from 1 to 10 nm. The variation range of t FL was based on the possible scale for practical devices while taking the covering trend of results into account. The focused parameters used for indicating the head stability performance, including the MR ratio, readback signal, dibit response, asymmetry parameter, and PSD profile, were analyzed and discussed.
The MR ratio of the CPP-GMR reader versus t FL is presented in Figure 2. It shows that the MR ratio increases at thicker t FL . Above a t FL of 6 nm, a change in layer thickness has less impact on the MR ratio increment than below. An enhancement of bulk spin-dependent scattering contributed to an increase in MR ratio. tion position at each varying time, tj, given in Equation (2) [39]. Then, the total PSD was computed by a summation of the local PSD at each partic frequency, Sx,y,z(ri, f), given as Equation (3). An integrated PSD can be further obtaine an integral of the overall PSD.

Results and Discussion
In this section, the output characteristics of the CPP-GMR read head were chara ized at different tFL from 1 to 10 nm. The variation range of tFL was based on the pos scale for practical devices while taking the covering trend of results into account. Th cused parameters used for indicating the head stability performance, including the ratio, readback signal, dibit response, asymmetry parameter, and PSD profile, were lyzed and discussed.
The MR ratio of the CPP-GMR reader versus tFL is presented in Figure 2. It shows the MR ratio increases at thicker tFL. Above a tFL of 6 nm, a change in layer thickness less impact on the MR ratio increment than below. An enhancement of bulk spin-dep ent scattering contributed to an increase in MR ratio. To characterize the readback response of the CPP-GMR reader, we investigated readback signal of the reader at tFL of 1 to 10 nm. Examples of readback signal wavefo for tFL of 1, 3, 5, and 8 nm are illustrated in Figure 3. The reader with a tFL of 8 nm app to have the highest distortion in the readback signal waveform. Meanwhile, the read signals of the readers with tFL of 3 and 5 nm are well patterned and symmetric. Howe it is generally insufficient to analyze the readback response through only an investiga of the readback waveform. We therefore characterized more insights related to the r back signal behavior, which are the dibit response, asymmetry parameter, and the profile. These parameters usually correspond to the stability performance of the read sors. To characterize the readback response of the CPP-GMR reader, we investigated the readback signal of the reader at t FL of 1 to 10 nm. Examples of readback signal waveforms for t FL of 1, 3, 5, and 8 nm are illustrated in Figure 3. The reader with a t FL of 8 nm appears to have the highest distortion in the readback signal waveform. Meanwhile, the readback signals of the readers with t FL of 3 and 5 nm are well patterned and symmetric. However, it is generally insufficient to analyze the readback response through only an investigation of the readback waveform. We therefore characterized more insights related to the readback signal behavior, which are the dibit response, asymmetry parameter, and the PSD profile. These parameters usually correspond to the stability performance of the read sensors.
The dibit response of the readback signal was obtained though the 63-bit PRBS with the polynomial x 6 + x 5 + 1. The main echoes related to this response are C (2) 1 and C (2) 2 , which are located at bits 27 and 22, respectively. These echoes typically indicate the nonlinear distortion of the readback waveform due to reader asymmetry [37]. It is noted that the impacts of higher orders of echoes were dominated by these main echoes and can be neglected in the evaluations. Figure 4a demonstrates the examples of dibit extraction of the reader with t FL of 1, 3, 5, and 8 nm. Each echo is magnified in the insets. The readers having a t FL of 5 and 8 nm seem to have higher echo amplitudes than others. Further details of echoes' amplitudes were, in addition, analyzed at all possible t FL , as shown in Figure 4b. When the t FL was increased starting from 1 nm, the amplitude of the echoes decreased until it reached its lowest scale. Then, the amplitude of echoes increased continuously when the t FL increased beyond the point providing the lowest echo amplitude. A variation of t FL appears to have a minor impact on C (2) 1 and C (2) 2 at a t FL above 6 nm, indicating a lesser affectation on the readback signal distortion for this specific range. The dibit response of the readback signal was obtained though the 63-bit PRBS the polynomial x 6 + x 5 + 1. The main echoes related to this response are C (2) 1 and C (2) 2, w are located at bits 27 and 22, respectively. These echoes typically indicate the non-li distortion of the readback waveform due to reader asymmetry [37]. It is noted that impacts of higher orders of echoes were dominated by these main echoes and can be glected in the evaluations. Figure 4a demonstrates the examples of dibit extraction o reader with tFL of 1, 3, 5, and 8 nm. Each echo is magnified in the insets. The readers ha a tFL of 5 and 8 nm seem to have higher echo amplitudes than others. Further detai echoes' amplitudes were, in addition, analyzed at all possible tFL, as shown in Figure  When the tFL was increased starting from 1 nm, the amplitude of the echoes decre until it reached its lowest scale. Then, the amplitude of echoes increased continuo when the tFL increased beyond the point providing the lowest echo amplitude. A varia of tFL appears to have a minor impact on C (2) 1 and C (2) 2 at a tFL above 6 nm, indicati lesser affectation on the readback signal distortion for this specific range.  The dibit response of the readback signal was obtained though the 63the polynomial x 6 + x 5 + 1. The main echoes related to this response are C (2) 1 a are located at bits 27 and 22, respectively. These echoes typically indicate distortion of the readback waveform due to reader asymmetry [37]. It is impacts of higher orders of echoes were dominated by these main echoes a glected in the evaluations. Figure 4a demonstrates the examples of dibit ex reader with tFL of 1, 3, 5, and 8 nm. Each echo is magnified in the insets. The r a tFL of 5 and 8 nm seem to have higher echo amplitudes than others. Fur echoes' amplitudes were, in addition, analyzed at all possible tFL, as shown When the tFL was increased starting from 1 nm, the amplitude of the ech until it reached its lowest scale. Then, the amplitude of echoes increased when the tFL increased beyond the point providing the lowest echo amplitud of tFL appears to have a minor impact on C (2) 1 and C (2) 2 at a tFL above 6 nm lesser affectation on the readback signal distortion for this specific range.  The asymmetry parameter of the readback signal obtained from the CPP-GMR reader was examined at different t FL , as shown in Figure 5. Most readers, except for those with a t FL of 6 and 7 nm, were found to contain under 10% readback signal asymmetry. The readback waveforms produced by the readers with a t FL of 4 and 9 nm are the most symmetric. From analysis of the readback signal, its dibit extraction, and its asymmetry parameter, it is obviously seen that the most suitable thickness of the free layer is 3 nm. The reader with this thickness value could provide the greatest pattern of readback signal.
Micromachines 2021, 12, x 6 The asymmetry parameter of the readback signal obtained from the CPP-GMR re was examined at different tFL, as shown in Figure 5. Most readers, except for those w tFL of 6 and 7 nm, were found to contain under 10% readback signal asymmetry. The r back waveforms produced by the readers with a tFL of 4 and 9 nm are the most symme From analysis of the readback signal, its dibit extraction, and its asymmetry paramet is obviously seen that the most suitable thickness of the free layer is 3 nm. The reader this thickness value could provide the greatest pattern of readback signal. In addition, the PSD profile of the head response was characterized as another st ity indicator for the reader. Figure 6a illustrates the integrated PSD at various tFL, whi frequency spectrum is indicated in Figure 6b. The PSD scale was found to be continuo lowered as the tFL was reduced from 10 to 3 nm. Below tFL = 3 nm, an adjustment of th causes a slight change in PSD amplitude. Then, it is worth reducing the thickness o free layer to 3 nm. The frequency spectrum of PSD of the readers with tFL of 1, 3, 5, a nm is demonstrated in Figure 6b. Corresponding to Figure 6a, the amplitude of PSD comes smaller at greater tFL. In particular, we found that the spectral peak is shifte higher frequencies by decreasing the tFL. This frequency shifting behavior can be descr by the magnetization precession which is computed by the LLGS equation [33,34]. LLGS formula generally consists of the precession, damping, and spin torque terms. spectral peak theoretically occurs depending mainly on the precession and dam terms of the time-varying magnetization. As the tFL is reduced, the spin torque term which its direction is opposing the magnetization precession becomes higher. This acc ingly causes an enhancement of the force pulling the magnetization towards the opp direction to its initial state. The resulting force therefore yields the higher oscillation o magnetization precession. Rather than the frequency shifting, the higher PSD intensi greater tFL indicates a stronger impact on the reader stability, as this typically implies stable magnetization precession and may further reduce the signal-to-noise ratio o read sensors. In addition, the PSD profile of the head response was characterized as another stability indicator for the reader. Figure 6a illustrates the integrated PSD at various t FL , while its frequency spectrum is indicated in Figure 6b. The PSD scale was found to be continuously lowered as the t FL was reduced from 10 to 3 nm. Below t FL = 3 nm, an adjustment of the t FL causes a slight change in PSD amplitude. Then, it is worth reducing the thickness of the free layer to 3 nm. The frequency spectrum of PSD of the readers with t FL of 1, 3, 5, and 8 nm is demonstrated in Figure 6b. Corresponding to Figure 6a, the amplitude of PSD becomes smaller at greater t FL . In particular, we found that the spectral peak is shifted to higher frequencies by decreasing the t FL . This frequency shifting behavior can be described by the magnetization precession which is computed by the LLGS equation [33,34]. The LLGS formula generally consists of the precession, damping, and spin torque terms. The spectral peak theoretically occurs depending mainly on the precession and damping terms of the time-varying magnetization. As the t FL is reduced, the spin torque term in which its direction is opposing the magnetization precession becomes higher. This accordingly causes an enhancement of the force pulling the magnetization towards the opposite direction to its initial state. The resulting force therefore yields the higher oscillation of the magnetization precession. Rather than the frequency shifting, the higher PSD intensity at greater t FL indicates a stronger impact on the reader stability, as this typically implies less stable magnetization precession and may further reduce the signal-to-noise ratio of the read sensors.
In summary, as the narrower physical reader gap of the read sensors is required to reach higher ADs, reducing the thickness of the free layer is therefore another approach to achieve this requirement. A very thin free layer, on the other hand, may result in an insufficient MR ratio. Then, in order to provide effective signal processing, an adequate MR ratio must be maintained. Our analysis shows that although a thinner free layer could provide a better readback response, the MR ratio is also reduced. Based on the trade-off between all characterized parameters, we believe that the appropriate t FL of this particular CPP-GMR reader is 3 nm. At this point, a reasonable MR ratio of 26% is sufficient for practical devices. The highest stability performance of the reader with a t FL of 3 nm was also confirmed through the analysis of the readback response that it is worthwhile to reduce the t FL to 3 nm. In summary, as the narrower physical reader gap of the read sensors is require reach higher ADs, reducing the thickness of the free layer is therefore another appro to achieve this requirement. A very thin free layer, on the other hand, may result i insufficient MR ratio. Then, in order to provide effective signal processing, an adeq MR ratio must be maintained. Our analysis shows that although a thinner free layer co provide a better readback response, the MR ratio is also reduced. Based on the trade between all characterized parameters, we believe that the appropriate tFL of this partic CPP-GMR reader is 3 nm. At this point, a reasonable MR ratio of 26% is sufficien practical devices. The highest stability performance of the reader with a tFL of 3 nm also confirmed through the analysis of the readback response that it is worthwhile to duce the tFL to 3 nm.

Conclusions
In this work, we investigated the dependence of the tFL on the stability performa of the CMFG Heusler-based CPP-GMR sensor targeted for an areal density of 1 Tb Simulations were done based on micromagnetic modelling. It was found that the tFL h highly influential impact on the MR ratio at tFL below 6 nm. A consideration of the r back signal of the head, including its dibit extraction and asymmetry parameter, indic that the reader having a tFL of 3 nm could produce a greatly patterned readback wavefo The PSD profile and its frequency spectrum are, in addition, analyzed and discusse confirm the worthiness of setting the tFL to 3 nm. Results also showed that a reason large MR ratio of 26% was greatly maintained at a tFL of 3 nm. Therefore, the trade

Conclusions
In this work, we investigated the dependence of the t FL on the stability performance of the CMFG Heusler-based CPP-GMR sensor targeted for an areal density of 1 Tb/in 2 . Simulations were done based on micromagnetic modelling. It was found that the t FL has a highly influential impact on the MR ratio at t FL below 6 nm. A consideration of the readback signal of the head, including its dibit extraction and asymmetry parameter, indicates that the reader having a t FL of 3 nm could produce a greatly patterned readback waveform. The PSD profile and its frequency spectrum are, in addition, analyzed and discussed to confirm the worthiness of setting the t FL to 3 nm. Results also showed that a reasonably large MR ratio of 26% was greatly maintained at a t FL of 3 nm. Therefore, the trade-off between all evaluated parameters suggests that this particular CPP-GMR reader with a t FL of 3 nm indicates the best stability performance. Findings can be utilized to design the CPP-GMR reader for use in ultrahigh areal densities of magnetic data storage.